During a visit to Seoul, the American defense secretary, Lloyd Austin, is bearing a clear message for hawkish South Koreans: We’ll cover you with our nuclear umbrella.

While parrying rising demands among South Koreans to be able to counter North Korea’s nuclear threats with nukes of their own, Mr. Austin is also focusing on upcoming joint exercises that are sure to outrage the North Koreans. He’s seeing South Korea’s defense minister, Lee Jong-sup, according to Seoul’s Yonhap News, to review “a full range of military capabilities, including nuclear.”

Mr. Austin’s visit will undoubtedly strengthen an alliance that has the enthusiastic backing of the South’s conservative president, Yoon Suk-yeol. At the same time, the secretary must convince skeptical South Koreans that they can count on America to defend them with a full panoply of weapons, including nuclear, if North Korea’s dictator ever makes good on his repeated threats of attack.

Mr. Yoon and his ministers are likely to accept that assurance at more or less face value, but they’re well aware of rising voices in the South repeating calls to “go nuclear.” A recent poll of a thousand South Koreans conducted by the Chey Institute for Advanced Study at Seoul showed 76.6 percent believe the South should explore its own nuclear weapons program.

The argument in favor of going nuclear, according to the results, is that the South needs “independently to counter Pyongyang’s intensifying nuclear threats and deter its provocations.” The poll also showed 72.4 percent of respondents believe South Korea is “capable of developing its own nuclear weapons.” Mr. Yoo, who wants to expand South Korea’s nuclear power program, has spoken of the need to consider the “option” for nuclear weapons.

For Mr. Austin, South Korea is the first stop before he goes on to another ally, the Philippines, whose enthusiasm about the American alliance has waned markedly in recent years. The Philippines president, Ferdinand “Bongbong” Marcos Jr., has called on China’s president, building on the premise that the Philippines has to get along with China while China claims control over the South China Sea.

One topic on the agenda during Mr. Austin’s talks in Seoul and Manila is Taiwan, the off-shore island province that Washington has promised to defend. Washington maintains an “institute” on Taiwan but no formal diplomatic relations, recognizing the island as belonging to China in keeping with the policy of “strategic ambiguity.”

South Korea, not wanting to offend China, has been careful not to adopt a strong stance on Taiwan, but Americans are increasingly wary about the Chinese threat in view of intimidation exercises by Chinese planes and warships, occasionally within Taiwan’s territorial waters.

Most recently, General Mike Minihan, head of the U.S. Air Mobility Command, has warned of war with Taiwan within five years. “I hope I am wrong,” NBC News quoted him as telling his subordinates in a memo. “My gut tells me we will fight in 2025.” He said China’s president might choose 2025 as the year to go to war for Taiwan while America was “distracted” by the 2024 presidential election.

That observation, though, was highly controversial. The Pentagon promptly disclaimed it, saying it was “not representative of the department’s view,” while Republican and Democratic congressmen debated the chances. Differences broke down along party lines.

The Texas Republican who is chairman of the House Foreign Affairs Committee, Michael McCaul, predicted on “Fox News Sunday” that China is “going to look at a military invasion” while President Biden “projected weakness.” A Democrat of Washington, Adam Smith, said a Chinese attack on Taiwan was “not only not inevitable” but “highly unlikely.”